Chapter 9 - Trigonometric Identities, Models, and Complex Numbers - 9.6 Complex Numbers and De Moivre's Theorem - Exercises and Problems for Section 9.6 - Exercises and Problems - Page 392: 1

$5e^{i \pi}$

The given complex number is $-5$. It can be written in the complex form $z=x+i y$ as: $z=-5+0i$ We see that in the complex plane the $x$-coordinate is $-5$ and the $y$-coordinate is $0$. So, we have: $r=|z|=\sqrt {(-5)^2+(0)^2}=5$ and $\theta=\tan^{-1} (\dfrac{0}{-5})=\pi-\tan^{-1} (0)=\pi-0=\pi$ $z$ lies on the negative side of the x-axis. Therefore, we have: $z=re^{i \theta}=5e^{i \pi}$